Absence of Spin Liquid in the Hubbard model on the Honeycomb Lattice

TL;DR

This study investigates the Hubbard model on the honeycomb lattice to determine if a spin liquid phase exists, concluding that no such phase is realized due to the magnetic transition occurring before the metal-insulator transition.

Contribution

The paper demonstrates that in the half-filled Hubbard model on the honeycomb lattice, a spin liquid state does not emerge, with magnetic order appearing prior to the metal-insulator transition.

Findings

Magnetic transition occurs at a lower interaction strength than the metal-insulator transition.

No non-magnetic insulating (spin liquid) state is observed.

The system transitions directly from semi-metallic to magnetic insulating state.

Abstract

The possible emergence of a spin liquid phase in the half-filled Hubbard model on the honeycomb lattice; a simple model of graphene, is studied using the variational cluster approximation. We found that the critical interaction strength of a magnetic transition is slightly lower than that of the non-magnetic metal-to-insulator transition. Thus a semi-metallic state becomes a magnetic insulator as the interaction strength increases and a non-magnetic insulating state does not occur. Therefore a spin liquid state characterized by an insulating state without long range order, is not realized in this system.